TY - JOUR
T1 - Exploding solitons and Shil'nikov's theorem
AU - Akhmediev, Nail
AU - Soto-Crespo, J. M.
PY - 2003/10/20
Y1 - 2003/10/20
N2 - We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.
AB - We have performed a detailed linear stability analysis of exploding solitons of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We have found, numerically, the whole set of perturbation eigenvalues for these solitons. We propose a scenario of soliton evolution based on this spectrum of eigenvalues. We relate exploding and self-restoring behavior of solitons to the Shil'nikov theorem, and point out common features and differences between our system, with an infinite number of degrees of freedom, and Shil'nikov's system with three degrees of freedom.
KW - Complex Ginzburg-Landau equation
KW - Dissipative solitons
UR - http://www.scopus.com/inward/record.url?scp=0142059923&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2003.08.060
DO - 10.1016/j.physleta.2003.08.060
M3 - Article
SN - 0375-9601
VL - 317
SP - 287
EP - 292
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 3-4
ER -